Modeling and Analysis of Some Heavy Tailed Time Series

The thesis has covered various aspects of modeling and analysis of finite mean time series with symmetric stable distributed innovations. Time series analysis based on Box and Jenkins methods are the most popular approaches where the models are linear and errors are Gaussian. We highlighted the limitations of classical time series analysis tools and explored some generalized tools and organized the approach parallel to the classical set up. In the present thesis we mainly studied the estimation and prediction of signal plus noise model. Here we assumed the signal and noise follow some models with symmetric stable innovations.We start the thesis with some motivating examples and application areas of alpha stable time series models. Classical time series analysis and corresponding theories based on finite variance models are extensively discussed in second chapter. We also surveyed the existing theories and methods correspond to infinite variance models in the same chapter. We present a linear filtering method for computing the filter weights assigned to the observation for estimating unobserved signal under general noisy environment in third chapter. Here we consider both the signal and the noise as stationary processes with infinite variance innovations. We derived semi infinite, double infinite and asymmetric signal extraction filters based on minimum dispersion criteria. Finite length filters based on Kalman-Levy filters are developed and identified the pattern of the filter weights. Simulation studies show that the proposed methods are competent enough in signal extraction for processes with infinite variance.Parameter estimation of autoregressive signals observed in a symmetric stable noise environment is discussed in fourth chapter. Here we used higher order Yule-Walker type estimation using auto-covariation function and exemplify the methods by simulation and application to Sea surface temperature data. We increased the number of Yule-Walker equations and proposed a ordinary least square estimate to the autoregressive parameters. Singularity problem of the auto-covariation matrix is addressed and derived a modified version of the Generalized Yule-Walker method using singular value decomposition.In fifth chapter of the thesis we introduced partial covariation function as a tool for stable time series analysis where covariance or partial covariance is ill defined. Asymptotic results of the partial auto-covariation is studied and its application in model identification of stable auto-regressive models are discussed. We generalize the Durbin-Levinson algorithm to include infinite variance models in terms of partial auto-covariation function and introduce a new information criteria for consistent order estimation of stable autoregressive model.In chapter six we explore the application of the techniques discussed in the previous chapter in signal processing. Frequency estimation of sinusoidal signal observed in symmetric stable noisy environment is discussed in this context. Here we introduced a parametric spectrum analysis and frequency estimate using power transfer function. Estimate of the power transfer function is obtained using the modified generalized Yule-Walker approach. Another important problem in statistical signal processing is to identify the number of sinusoidal components in an observed signal. We used a modified version of the proposed information criteria for this purpose.

Recurrence Quantification Analysis of System Signals for Detecting Tool and Chatter in Turning

In this thesis, the applications of the recurrence quantification analysis in metal cutting operation in a lathe, with specific objective to detect tool wear and chatter, are presented.This study is based on the discovery that process dynamics in a lathe is low dimensional chaotic. It implies that the machine dynamics is controllable using principles of chaos theory. This understanding is to revolutionize the feature extraction methodologies used in condition monitoring systems as conventional linear methods or models are incapable of capturing the critical and strange behaviors associated with the metal cutting process.As sensor based approaches provide an automated and cost effective way to monitor and control, an efficient feature extraction methodology based on nonlinear time series analysis is much more demanding. The task here is more complex when the information has to be deduced solely from sensor signals since traditional methods do not address the issue of how to treat noise present in real-world processes and its non-stationarity. In an effort to get over these two issues to the maximum possible, this thesis adopts the recurrence quantification analysis methodology in the study since this feature extraction technique is found to be robust against noise and stationarity in the signals.The work consists of two different sets of experiments in a lathe; set-I and set-2. The experiment, set-I, study the influence of tool wear on the RQA variables whereas the set-2 is carried out to identify the sensitive RQA variables to machine tool chatter followed by its validation in actual cutting. To obtain the bounds of the spectrum of the significant RQA variable values, in set-i, a fresh tool and a worn tool are used for cutting. The first part of the set-2 experiments uses a stepped shaft in order to create chatter at a known location. And the second part uses a conical section having a uniform taper along the axis for creating chatter to onset at some distance from the smaller end by gradually increasing the depth of cut while keeping the spindle speed and feed rate constant.The study concludes by revealing the dependence of certain RQA variables; percent determinism, percent recurrence and entropy, to tool wear and chatter unambiguously. The performances of the results establish this methodology to be viable for detection of tool wear and chatter in metal cutting operation in a lathe. The key reason is that the dynamics of the system under study have been nonlinear and the recurrence quantification analysis can characterize them adequately.This work establishes that principles and practice of machining can be considerably benefited and advanced from using nonlinear dynamics and chaos theory.

Development of Electrochemical Sensors for Various Pharmaceuticals

The development of electrochemical sensors is currently one of the active areas of research in analytical chemistry.Voltammetric sensors as an important class of electrochemical sensors are extensively used in pharmaceutical applications.In voltammetric analysis,many active compounds in dosage forms,in contrast to excipients,can be readily oxidised or reduced at the electrode surface by applying a potential.Chemically modified electrodes have great significance in the electrochemical determination of pharmaceuticals.The modification of electrode results in efficient determination of electroactive species at very lower potential without any major interferences.The present study involves the fabrication of 8 voltammetric sensors for the drugs Metronidazole Benzoate, Sulfamethoxazole, Acyclovir, Pam Chloride , Trimethoprim , Tamsulosin Hydrochloride and Ceftriaxone Sodium.Two sensors were developed for the drug tamsulosin hydrochloride while one sensor each was developed for the other drugs.

Analysis of System Signals Based on Cross Recurrence Method for System Dynamics Characterization

Natural systems are inherently non linear. Recurrent behaviours are typical of natural systems. Recurrence is a fundamental property of non linear dynamical systems which can be exploited to characterize the system behaviour effectively. Cross recurrence based analysis of sensor signals from non linear dynamical system is presented in this thesis. The mutual dependency among relatively independent components of a system is referred as coupling. The analysis is done for a mechanically coupled system specifically designed for conducting experiment. Further, cross recurrence method is extended to the actual machining process in a lathe to characterize the chatter during turning. The result is verified by permutation entropy method. Conventional linear methods or models are incapable of capturing the critical and strange behaviours associated with the dynamical process. Hence any effective feature extraction methodologies should invariably gather information thorough nonlinear time series analysis. The sensor signals from the dynamical system normally contain noise and non stationarity. In an effort to get over these two issues to the maximum possible extent, this work adopts the cross recurrence quantification analysis (CRQA) methodology since it is found to be robust against noise and stationarity in the signals. The study reveals that the CRQA is capable of characterizing even weak coupling among system signals. It also divulges the dependence of certain CRQA variables like percent determinism, percent recurrence and entropy to chatter unambiguously. The surrogate data test shows that the results obtained by CRQA are the true properties of the temporal evolution of the dynamics and contain a degree of deterministic structure. The results are verified using permutation entropy (PE) to detect the onset of chatter from the time series. The present study ascertains that this CRP based methodology is capable of recognizing the transition from regular cutting to the chatter cutting irrespective of the machining parameters or work piece material. The results establish this methodology to be feasible for detection of chatter in metal cutting operation in a lathe.

Development of Macrocyclics based Electrochemical Sensors

Electroanalytical techniques represent a class of powerful and versatile analytical method which is based on the electrical properties of a solution of the analyte when it is made part of an electrochemical cell. They offer high sensitivity, accuracy, precision and a large linear dynamic range. The cost of instrumentation is relatively low compared to other instrumental methods of analysis. Many solid state electrochemical sensors have been commercialised nowadays. Potentiometry is a very simple electroanalytical technique with extraordinary analytical capabilities. Since valinomycin was introduced as an ionophore for K+, Ion Selective Electrodes have become one of the best studied and understood analytical devices. It can be used for the determination of substances ranging from simple inorganic ions to complex organic molecules. It is a very attractive option owing to the wide range of applications and ease of the use of the instruments employed. They also possess the advantages of short response time, high selectivity and very low detection limits. Moreover, analysis by these electrodes is non-destructive and adaptable to small sample volumes. It has become a standard technique for medical researchers, biologists, geologists and environmental specialists. This thesis presents the synthesis and characterisation of five ionophores. Based on these ionophores, nine potentiometric sensors are fabricated for the determination of ions such as Pb2+, Mn2+, Ni2+, Cu2+ and Sal- ion (Salicylate ion). The electrochemical characterisation and analytical application studies of the developed sensors are also described. The thesis is divided into eight chapters

Effect of long-range Coulomb interaction on shot-noise suppression in ballistic transport

We present a microscopic analysis of shot-noise suppression due to long-range Coulomb interaction in semiconductor devices under ballistic transport conditions. An ensemble Monte Carlo simulator self-consistently coupled with a Poisson solver is used for the calculations. A wide range of injection-rate densities leading to different degrees of suppression is investigated. A sharp tendency of noise suppression at increasing injection densities is found to scale with a dimensionless Debye length related to the importance of space-charge effects in the structure.

Development of a Fully Automated Image Analysis Method for High Density cDNA and array CGH Microarray Based Genomic Studies

In this thesis, different techniques for image analysis of high density microarrays have been investigated. Most of the existing image analysis techniques require prior knowledge of image specific parameters and direct user intervention for microarray image quantification. The objective of this research work was to develop of a fully automated image analysis method capable of accurately quantifying the intensity information from high density microarrays images. The method should be robust against noise and contaminations that commonly occur in different stages of microarray development.

Implementation of a Neural Network Classifier for Noise Sources in the Ocean

The paper investigates the feasibility of implementing an intelligent classifier for noise sources in the ocean, with the help of artificial neural networks, using higher order spectral features. Non-linear interactions between the component frequencies of the noise data can give rise to certain phase relations called Quadratic Phase Coupling (QPC), which cannot be characterized by power spectral analysis. However, bispectral analysis, which is a higher order estimation technique, can reveal the presence of such phase couplings and provide a measure to quantify such couplings. A feed forward neural network has been trained and validated with higher order spectral features

Novel Electrochemical and Fluorescence Sensors for Food Additives and Neurotransmitters

There is an enormous demand for chemical sensors in many areas and disciplines including chemistry, biology, clinical analysis, environmental science. Chemical sensing refers to the continuous monitoring of the presence of chemical species and is a rapidly developing field of science and technology. They are analytical devices which transform chemical information generating from a reaction of the analyte into an measurable signal. Due to their high selectivity, sensitivity, fast response and low cost, electrochemical and fluorescent sensors have attracted great interest among the researchers in various fields. Development of four electrochemical sensors and three fluorescent sensors for food additives and neurotransmitters are presented in the thesis. Based on the excellent properties of multi walled carbon nanotube (MWCNT), poly (L-cysteine) and gold nanoparticles (AuNP) four voltammetric sensors were developed for various food additives like propyl gallate, allura red and sunset yellow. Nanosized fluorescent probes including gold nanoclusters (AuNCs) and CdS quantum dots (QDs) were used for the fluorescent sensing of butylated hydroxyanisole, dopamine and norepinephrine. A total of seven sensors including four electrochemical sensors and three fluorescence sensors have been developed for food additives and neurotransmitters.

Development of Electrochemical and Fluorescent Sensors

Chemical sensors have growing interest in the determination of food additives, which are creating toxicity and may cause serious health concern, drugs and metal ions. A chemical sensor can be defined as a device that transforms chemical information, ranging from the concentration of a specific sample component to total composition analysis, into an analytically useful signal. The chemical information may be generated from a chemical reaction of the analyte or from a physical property of the system investigated. Two main steps involved in the functioning of a chemical sensor are recognition and transduction. Chemical sensors employ specific transduction techniques to yield analyte information. The most widely used techniques employed in chemical sensors are optical absorption, luminescence, redox potential etc. According to the operating principle of the transducer, chemical sensors may be classified as electrochemical sensors, optical sensors, mass sensitive sensors, heat sensitive sensors etc. Electrochemical sensors are devices that transform the effect of the electrochemical interaction between analyte and electrode into a useful signal. They are very widespread as they use simple instrumentation, very good sensitivity with wide linear concentration ranges, rapid analysis time and simultaneous determination of several analytes. These include voltammetric, potentiometric and amperometric sensors. Fluorescence sensing of chemical and biochemical analytes is an active area of research. Any phenomenon that results in a change of fluorescence intensity, anisotropy or lifetime can be used for sensing. The fluorophores are mixed with the analyte solution and excited at its corresponding wavelength. The change in fluorescence intensity (enhancement or quenching) is directly related to the concentration of the analyte. Fluorescence quenching refers to any process that decreases the fluorescence intensity of a sample. A variety of molecular rearrangements, energy transfer, ground-state complex formation and collisional quenching. Generally, fluorescence quenching can occur by two different mechanisms, dynamic quenching and static quenching. The thesis presents the development of voltammetric and fluorescent sensors for the analysis of pharmaceuticals, food additives metal ions. The developed sensors were successfully applied for the determination of analytes in real samples. Chemical sensors have multidisciplinary applications. The development and application of voltammetric and optical sensors continue to be an exciting and expanding area of research in analytical chemistry. The synthesis of biocompatible fluorophores and their use in clinical analysis, and the development of disposable sensors for clinical analysis is still a challenging task. The ability to make sensitive and selective measurements and the requirement of less expensive equipment make electrochemical and fluorescence based sensors attractive.

An Analysis of the Effect of Gaussian Error in Object Recognition

Object recognition is complicated by clutter, occlusion, and sensor error. Since pose hypotheses are based on image feature locations, these effects can lead to false negatives and positives. In a typical recognition algorithm, pose hypotheses are tested against the image, and a score is assigned to each hypothesis. We use a statistical model to determine the score distribution associated with correct and incorrect pose hypotheses, and use binary hypothesis testing techniques to distinguish between them. Using this approach we can compare algorithms and noise models, and automatically choose values for internal system thresholds to minimize the probability of making a mistake.

The representation of conditional expectations of non-Gaussian noise

For Wiener spaces conditional expectations and $L^{2}$-martingales w.r.t. the natural filtration have a natural representation in terms of chaos expansion. In this note an extension to larger classes of processes is discussed. In particular, it is pointed out that orthogonality of the chaos expansion is not required.

Can the frequency of blocking be described by a red noise process?

The frequency of persistent atmospheric blocking events in the 40-yr ECMWF Re-Analysis (ERA-40) is compared with the blocking frequency produced by a simple first-order Markov model designed to predict the time evolution of a blocking index [defined by the meridional contrast of potential temperature on the 2-PVU surface (1 PVU ≡ 1 × 10−6 K m2 kg−1 s−1)]. With the observed spatial coherence built into the model, it is able to reproduce the main regions of blocking occurrence and the frequencies of sector blocking very well. This underlines the importance of the climatological background flow in determining the locations of high blocking occurrence as being the regions where the mean midlatitude meridional potential vorticity (PV) gradient is weak. However, when only persistent blocking episodes are considered, the model is unable to simulate the observed frequencies. It is proposed that this persistence beyond that given by a red noise model is due to the self-sustaining nature of the blocking phenomenon.

A geostatistical analysis of soil, vegetation, and image data characterizing land surface variation

The elucidation of spatial variation in the landscape can indicate potential wildlife habitats or breeding sites for vectors, such as ticks or mosquitoes, which cause a range of diseases. Information from remotely sensed data could aid the delineation of vegetation distribution on the ground in areas where local knowledge is limited. The data from digital images are often difficult to interpret because of pixel-to-pixel variation, that is, noise, and complex variation at more than one spatial scale. Landsat Thematic Mapper Plus (ETM+) and Satellite Pour l'Observation de La Terre (SPOT) image data were analyzed for an area close to Douna in Mali, West Africa. The variograms of the normalized difference vegetation index (NDVI) from both types of image data were nested. The parameters of the nested variogram function from the Landsat ETM+ data were used to design the sampling for a ground survey of soil and vegetation data. Variograms of the soil and vegetation data showed that their variation was anisotropic and their scales of variation were similar to those of NDVI from the SPOT data. The short- and long-range components of variation in the SPOT data were filtered out separately by factorial kriging. The map of the short-range component appears to represent the patterns of vegetation and associated shallow slopes and drainage channels of the tiger bush system. The map of the long-range component also appeared to relate to broader patterns in the tiger bush and to gentle undulations in the topography. The results suggest that the types of image data analyzed in this study could be used to identify areas with more moisture in semiarid regions that could support wildlife and also be potential vector breeding sites.

Recent changes in solar outputs and the global mean surface temperature. III. Analysis of contributions to global mean air surface temperature rise

A multivariate fit to the variation in global mean surface air temperature anomaly over the past half century is presented. The fit procedure allows for the effect of response time on the waveform, amplitude and lag of each radiative forcing input, and each is allowed to have its own time constant. It is shown that the contribution of solar variability to the temperature trend since 1987 is small and downward; the best estimate is -1.3% and the 2sigma confidence level sets the uncertainty range of -0.7 to -1.9%. The result is the same if one quantifies the solar variation using galactic cosmic ray fluxes (for which the analysis can be extended back to 1953) or the most accurate total solar irradiance data composite. The rise in the global mean air surface temperatures is predominantly associated with a linear increase that represents the combined effects of changes in anthropogenic well-mixed greenhouse gases and aerosols, although, in recent decades, there is also a considerable contribution by a relative lack of major volcanic eruptions. The best estimate is that the anthropogenic factors contribute 75% of the rise since 1987, with an uncertainty range (set by the 2sigma confidence level using an AR(1) noise model) of 49–160%; thus, the uncertainty is large, but we can state that at least half of the temperature trend comes from the linear term and that this term could explain the entire rise. The results are consistent with the intergovernmental panel on climate change (IPCC) estimates of the changes in radiative forcing (given for 1961–1995) and are here combined with those estimates to find the response times, equilibrium climate sensitivities and pertinent heat capacities (i.e. the depth into the oceans to which a given radiative forcing variation penetrates) of the quasi-periodic (decadal-scale) input forcing variations. As shown by previous studies, the decadal-scale variations do not penetrate as deeply into the oceans as the longer term drifts and have shorter response times. Hence, conclusions about the response to century-scale forcing changes (and hence the associated equilibrium climate sensitivity and the temperature rise commitment) cannot be made from studies of the response to shorter period forcing changes.